No judgment about whether Google was right or not. Same for Lemoine.
As a career move for him, this only makes sense if he wants a brief, meteoric career in media or public advocacy. He can get articles published in The New Yorker and go on TV now. Maybe he can sue Google and get a settlement.
In five years, there will be AI systems much better than LaMDA and no one will return his calls.
He's got a name, whereas if he took the boring, traditional career path, he'd have to publish, give papers & speeches, and work his way up through the system. It depends on what you want out of life, I guess.